Hi Katelyn,
Find exact values for remaining trigonometric functions
a) sin θ = 1/3, cos θ < 0
To answer this, use a triangle drawn from the origin into the second quadrant (because that is where cosine is negative and sine positive) with a vertical leg of 1, a hypotenuse of three, and a horizontal leg of 2√2
You should get:
sin θ = 1/3
cos θ = -(2√2)/3
tan θ = -1/(2√2). (denominator should be rationalized to -√2/4 )
csc θ = 3
sec θ = -3/(2√2) (denominator should be rationalized to (-3√2)/4 )
cot θ = -2√2
b) tan θ = 1/2, π < θ < 3π /2
For this one the triangle(s) should be drawn from the origin into the third quadrant (so θ is in the specified interval) with a horizontal leg of 2, a vertical leg of 1, and that will make the hypotenuse √5.
Then the trig ratios should be:
Sinθ = -1/√5 -√5/5
cosθ = -2/√5 (-2√5)/5
tanθ = 1/2
cscθ = -√5
secθ = -√5/2
cot θ = 2
